Topics in Elementary Geometry

This small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which have b...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bottema, O. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2008.
Edición:2nd ed. 2008.
Temas:
Geometry.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • The Pythagorean Theorem
  • Ceva#x02019;s Theorem
  • Perpendicular Bisectors; Concurrence
  • The Nine-Point Circle and Euler Line
  • The Taylor Circle
  • Coordinate Systems with Respect to a Triangle
  • The Area of a Triangle as a Function of the Barycentric Coordinates of Its Vertices
  • The Distances from a Point to the Vertices of a Triangle
  • The Simson Line
  • Morley#x02019;s Triangle
  • Inequalities in a Triangle
  • The Mixed Area of Two Parallel Polygons
  • The Isoperimetric Inequality
  • Poncelet Polygons
  • A Closure Problem for Triangles
  • A Class of Special Triangles
  • Two Unusual Conditions for a Triangle
  • A Counterpart for the Euler Line
  • Menelaus#x02019;s Theorem; Cross-Ratios and Reciprocation
  • The Theorems of Desargues, Pappus, and Pascal
  • Inversion
  • The Theorems of Ptolemy and Casey
  • Pedal Triangles; Brocard Points
  • Isogonal Conjugation; the Symmedian Point
  • Isotomic Conjugation
  • Triangles with Two Equal Angle Bisectors
  • The Inscribed Triangle with the Smallest Perimeter; the Fermat Point.

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